In general, for an $n$-element set $A = \{ x_{n-1}, x_{n-2}, ..., x_1, x_0 \}$ we have that each subset $B \subseteq A$ has a unique sequence in this manner, $(a_{n-1}, a_{n-2}, ..., a_1, a_0)$ for $a_j \in \{0, 1 \}$ for all $j \in \{0, 1, ..., n-1 \}$ as described above and such that the binary digit representation $a_{n-1}a_{n-2}...a_1a_0$ gives a decimal ($10$-usable digit) number $m$ where $0 \leq m < 2^n$ obtained by the formula:

For example, suppose that we want to list all combinations of the elements in $A = \{x_2, x_1, x_0 \}$. There will be $2^3 = 8$ combinations. The table below illustrates the use of Theorem 1 to generate all $8$ of these combinations.